We investigate the effect of decoherence on Fano resonances in wave transmission through resonant scattering structures. We show that the Fano asymmetry parameter q follows, as a function of the strength of decoherence, trajectories in the complex plane that reveal detailed information on the underlying decoherence process. Dissipation and unitary dephasing give rise to manifestly different trajectories. Our predictions are successfully tested against microwave experiments using metal cavities with different absorption coefficients and against previously published data on transport through quantum dots. These results open up new possibilities for studying the effect of decoherence in a wide array of physical systems where Fano resonances are present.

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to ffiffiffiffi N p , where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density-namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains. Introduction.-Currently, one of the most fruitful branches of quantum information is the field of quantum search algorithms. It started with Grover's work [1] describing a search algorithm for unstructured databases, which has been implemented experimentally in NMR [2,3] and in optical experiments [4]. More recently, spatial quantum search algorithms have been proposed based on the quantum walk mechanism [5,6]. All of these algorithms can achieve up to quadratic speedup compared to the corresponding classical search. For quantum searches on generic d-dimensional lattices, certain restrictions have been observed, however, depending on whether the underlying quantum walk is discrete [7] or continuous [8]. While effective search algorithms for discrete walks on square lattices have been reported for d ≥ 2 [9,10], continuoustime quantum search algorithms on the same lattice show speedup compared to the classical search only for d ≥ 4 [11]. Experimental implementations of discrete quantum walks need time stepping mechanisms such as laser pulses [12][13][14][15][16][17]. By switching to a continuous-time evolution based, for example, on tight-binding coupling between sites, one can avoid time discretization in an experiment. It has been shown in Ref.[18] that continuous-time quantum search in 2D is indeed possible when performed near the Dirac point in graphene or, more generally, for lattices with a cone structure in the dispersion relation [19], i.e., a linear growth of the density of states (DOS). This effect adds a

The influence of absorption on the spectra of microwave graphs has been studied experimentally. The microwave networks were made up of coaxial cables and T junctions. First, absorption was introduced by attaching a 50Ω load to an additional vertex for graphs with and without time-reversal symmetry. The resulting level-spacing distributions were compared with a generalization of the Wigner surmise in the presence of open channels proposed recently by Poli et al. [Phys. Rev. Lett. 108, 174101 (2012)]. Good agreement was found using an effective coupling parameter. Second, absorption was introduced along one individual bond via a variable microwave attenuator, and the influence of absorption on the length spectrum was studied. The peak heights in the length spectra corresponding to orbits avoiding the absorber were found to be independent of the attenuation, whereas, the heights of the peaks belonging to orbits passing the absorber once or twice showed the expected decrease with increasing attenuation.

We present the first experimental observation of resonance-assisted tunneling, a wave phenomenon, where regular-to-chaotic tunneling is strongly enhanced by the presence of a classical nonlinear resonance chain. For this we use a microwave cavity made of oxygen free copper with the shape of a desymmetrized cosine billiard designed with a large nonlinear resonance chain in the regular region. It is opened in a region, where only chaotic dynamics takes place, such that the tunneling rate of a regular mode to the chaotic region increases the line width of the mode. Resonance-assisted tunneling is demonstrated by (i) a parametric variation and (ii) the characteristic plateau and peak structure towards the semiclassical limit. Tunneling describes the possibility of a quantum particle to transmit through a barrier into a region of space, which is inaccessible for a corresponding classical particle. It is a general wave phenomenon. Dynamical tunneling describes the tunneling of waves between classically disjoint regions of phase space, even without an energy barrier being present [1]. It occurs in several variants [2], e.g., from a regular region to the chaotic region [3][4][5][6][7][8][9], from a regular region via the chaotic region to another regular region [10][11][12][13][14][15][16], or between two chaotic regions [17][18][19]. It is essential for applications in atomic and molecular physics [20][21][22], ultracold atoms [15,16,23], optical cavities [24][25][26][27][28], quantum wells [29], and microwave resonators [7,14].We consider regular-to-chaotic tunneling, where the tunneling rate γ describes the decay |ψ reg (t)| 2 ∝ exp(−γt) of a quantum state, initially located within the regular region, to the chaotic region. Towards the semiclassical limit γ is determined by two main effects: For small wave numbers direct regular-to-chaotic tunneling typically leads to an exponential decrease of γ with increasing wave number [3,6,30]. For larger wave numbers resonance-assisted tunneling (RAT) drastically enhances the tunneling rates, causing the characteristic plateau and peak structures [31][32][33][34]. RAT occurs due to nonlinear resonance chains inside a regular region, see Fig. 1(b) (orange lines), which arise due to the Poincaré-Birkhoff theorem. A combined prediction for direct regular-tochaotic tunneling and RAT is given in Ref. [34].Several experiments were performed demonstrating